Grade: 8 Unit: 5 Week: 2 Content: Properties of Transformations Transformations and Congruency Dates: 3/11-3/14 (4 days)
Theme Essential Question: How are transformations a visual representation of an object moving in our three-dimensional world?
Essential Questions:
What properties of a figure are preserved under a translation, reflection, or rotation?
What is the connection between transformations and figures that have the same shape and size?
Standards
8.G.1 Verify experimentally the properties of rotations, reflections, and translations:
a. Lines are taken to lines, and line segments to line segments of the same length.
b. Angles are taken to angles of the same measure.
c. Parallel lines are taken to parallel lines.
8.G.2 Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.
Objectives
The student will verify the properties of a figure that are preserved under a translation, reflection or rotation.
The student will combine transformations and compare the size and shape of the final image.
The student will analyze and evaluate two-dimensional figures by rotation, reflection or translation to determine if they are congruent.
Reflections and/or Comments from your PCSSD 8th Grade Curriculum Team In this lesson, it is essential that students use various approaches to explore, study, and develop logical arguments in their investigations of properties of transformation. It is imperative students use such items as rulers and protractors, patty paper, TI84 geometry app (Cabri Jr.), and/or software such as GeoGebra or Geometer’s Sketchpad.
It is recommended that every student be exposed to the works of MCEscher. We have added an alternative product for the struggling-learner having difficulties with the creation of their individual MC Escher design.
Assessment Product Mathematics behind the Art of MC EscherExplore the transformations using principles of MC Escher from this website, and have students work to create a similar art project with examples of each type of transformation included. This will be an ongoing project over several weeks. Recommended schedule for project development:
Week 1: Students are to explore the principles of MC Escher.
Week 2: Students are to study the development of design and prepare their initial sketch.
Week 3: Students are finalizing their design work.
Week 4: Museum Walk.
Alternative Product: Park the Car Students are to plot a car 2 units by 4 units in quadrant I, they are to plot a garage 1 unit by 2 unit in quadrant III. They are to use each transformation at least once (translation, rotation, reflection, and dilation) to park their car into the garage. Each translation should be noted using correct notation with corresponding coordinates.
Key Questions
How do you verify experimentally the properties of rotations, reflections, and translations?
How can a two-dimensional figure be congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations?
Observable Student Behaviors
The student will provide a viable argument to justify the properties of rotations, reflections, and translations.
The student will compare the size and shape of the final image that has underwent combined transformations.
The student will connect transformations with congruency.
Mathematical Practices 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning.
Suggested Activities [see Legend to highlight MCO and HYS]
Houghton Mifflin OnCore Mathematics Middle School Grade 8 Unit 4.2-4.3, p. 95-98
ABC Mastering the Common Core in Mathematics 9.3-9.5, p. 135-141 and 12.3 189-194
Gizmo Lessons
8.G.1
Reflections
Reshape and resize a figure and examine how its reflection changes in response. Move the line of reflection and explore how the reflection is translated.
Rotations, Reflections and Translations
Rotate, reflect, and translate a figure in the plane. Compare the translated figure to the original figure.
Similar Figures-Activity A
Vary the scale factor and rotation of an image and compare it to the pre-image. Determine how the angle measures and side lengths of the two figures are related.
Translations
Translate a figure horizontally and vertically in the plane and examine the matrix representation of the translation.
Teaching the Common Core Math Standards with Hands-On Activities by Judith Muschla
G.1 p. 201
G.2 Activity 1 p. 205, Activity 2 p. 206
JBHM 8th GP3-p. 63-70, 73-78, 83-103
Glencoe Pre-Algebra – p. 500-504
Glencoe Algebra 1- p. 197-203
Highly Recommended:
http://illustrativemathematics.org/illustrations/646 (G.2)The Illustrative Mathematics Project offers guidance to states, assessment consortia, testing companies, and curriculum developers by illustrating the range and types of mathematical work that students will experience in a faithful implementation of the Common Core State Standards. The website features a clickable version of the Common Core in mathematics and the first round of "illustrations" of specific standards with associated classroom tasks and solutions.
Grade: 8 Unit: 5 Week: 2
Content: Properties of Transformations
Transformations and Congruency
Dates: 3/11-3/14 (4 days)
Theme Essential Question:
How are transformations a visual representation of an object moving in our three-dimensional world?
Essential Questions:
Standards
Objectives
Reflections and/or Comments from your PCSSD 8th Grade Curriculum Team
In this lesson, it is essential that students use various approaches to explore, study, and develop logical arguments in their investigations of properties of transformation. It is imperative students use such items as rulers and protractors, patty paper, TI84 geometry app (Cabri Jr.), and/or software such as GeoGebra or Geometer’s Sketchpad.
It is recommended that every student be exposed to the works of MCEscher. We have added an alternative product for the struggling-learner having difficulties with the creation of their individual MC Escher design.
Assessment
Product
Mathematics behind the Art of MC Escher Explore the transformations using principles of MC Escher from this website, and have students work to create a similar art project with examples of each type of transformation included. This will be an ongoing project over several weeks. Recommended schedule for project development:
Alternative Product: Park the Car
Students are to plot a car 2 units by 4 units in quadrant I, they are to plot a garage 1 unit by 2 unit in quadrant III. They are to use each transformation at least once (translation, rotation, reflection, and dilation) to park their car into the garage. Each translation should be noted using correct notation with corresponding coordinates.
Key Questions
Observable Student Behaviors
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
Suggested Activities [see Legend to highlight MCO and HYS]
- Houghton Mifflin OnCore Mathematics Middle School Grade 8 Unit 4.2-4.3, p. 95-98
- ABC Mastering the Common Core in Mathematics 9.3-9.5, p. 135-141 and 12.3 189-194
Gizmo Lessons- Highly Recommended:
http://illustrativemathematics.org/illustrations/646 (G.2)The Illustrative Mathematics Project offers guidance to states, assessment consortia, testing companies, and curriculum developers by illustrating the range and types of mathematical work that students will experience in a faithful implementation of the Common Core State Standards. The website features a clickable version of the Common Core in mathematics and the first round of "illustrations" of specific standards with associated classroom tasks and solutions.Diverse Learners
Homework
Suggested:
Terminology for Teachers
Ethnicity/Culture | Immigration/Migration | Intercultural Competence | Socialization | Racism/Discrimination
High Yield Strategies
Similarities/Differences | Summarizing/Notetaking | Reinforcing/Recognition | Homework/Practice |
Non-Linguistic representation | Cooperative Learning | Objectives/Feedback |
Generating-Testing Hypothesis | Cues, Questions, Organizers
Resources
Professional Texts
Literary Texts
Informational Texts
- See New York Common Core Aligned Task (other resources)
http://schools.nyc.gov/Academics/CommonCoreLibrary/SeeStudentWork/default.htmArt, Music, and Media
Manipulatives
Games
Videos
SMART Board Lessons, Promethean Lessons
- Smartboard Resource Website Smartboard lesson search engine
- 8.G. 1 Translation
The objectives are to translate figures in the coordinate plane and to describe the translation.- 8.G.1 Reflection
The objectives are to identify, describe and perform reflections in the coordinate plane.- 8.G. 2 Polygons and Patten Blocks
Use pattern blocks to explore the relationships between a variety of polygons. Explore similar and congruent shapes. Explore flips, slides, and turns.- 8.G. 2 Rotations, Translations, Reflections, and Dilations/Math by Ed
Rotations, Translations, Reflections, and DilationsWebsites
Other Activities, etc.
Language
Arts
Week 1
Week 2
Week 3
Week 4
Matrix
Week 1
Week 2
Week 3
Week 4
Home K-2
Home 3-6
Home 6-8
Unit 1
Unit 2
Unit 3
Unit 4